(f) Lovely Detergents Ltd is carrying out a research and development process in order to develop a new detergent, using an enzyme. The process consists of nine activities. The optimistic time (to), the pessimistic (tp), the most likely time (tm) and the precedence relationships are given in the table below. Activity Precedence Relationship To Tm Tp (Which activity comes before (Weeks) (Weeks) (weeks) the one in the first column ?) ABCD C 3 4 5 5 7 9 F 4 6 8 B,C 2 3 4 E B 6 7 14 F 2 4 6 GH EE 9 12 15 7 9 11 I F 5 60 13 Calculate the expected time for each activity. (ii) Draw the network. (5 marks) (5 marks) (iii) Calculate the standard deviation and variance for each activity. (iv) Calculate the expected project completion time. (4 marks) (2 marks) (v) What is the probability the project will be completed in 30 weeks? (vi) What is the probability the project will be completed in 23 weeks? (2 marks) (2 marks)